Overview. Hierarchy. Level of detail hierarchy Texture maps Procedural shading and texturing Texture synthesis and noise.

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1 Overview Level of detail hierarchy Texture maps Procedural shading and texturing Texture synthesis and noise Hierarchy Physics Computer Graphics Geometrical optics Macro-structures Transport Micro-structures Microfacets Physical optics Kirchoff approx. Quantum optics Geometry Displacement (P) maps Bump (N) maps Texels (BRDF) Texture Page 1

2 Texture Maps How is texture mapped to the surface? Dimensionality: 1D, 2D, 3D Texture coordinates (s,t) Surface parameters (u,v) Direction vectors: reflection R, normal N, halfway H Projection: cylinder Developable surface: polyhedral net Reparameterize a surface: old-fashion model decal What does texture control? Surface color and opacity Illumination functions: environment maps, shadow maps Reflection functions: reflectance maps Perturb geometry: bump and displacement maps History Catmull/Williams basic idea Blinn and Newell basic idea, reflection maps Blinn bump mapping Williams 1978, Reeves et al shadow maps Smith 1980, Heckbert texture mapped polygons Williams mipmaps Miller and Hoffman illumination and reflectance Perlin 1985, Peachey solid textures Greene environment maps/world projections Akeley Reality Engine Page 2

3 Tom Porter s Bowling Pin RenderMan Companion, Pls. 12 & 13 Direction Maps Many ways to map directions to images... Methods: Gazing Ball (N) Create by photographing a reflective sphere Fisheye Lens Standard camera lens Cubical Environment Map (R) Create with a rendering program, photography... Lattitude-Longitude (Map Projections) Create by painting Issues: Non-linear mapping - expensive, curved lines Area distortion - spatially varying resolution Convert between maps using image warp Page 3

4 Cubical Environment Map Note: Easy to produce with rendering system Possible to produce from photographs Uniform resolution Simple texture coordinates calculation Gazing Ball Note: Photograph of reflective ball Reflection indexed by normal Maps entire field of view to circle Resolution function of orientation; maximum head-on Alternatives: Fish eye, map projections Page 4

5 Reflectance Maps Integrate over a hemisphere: BRDF * L Very low resolution often sufficient: At NYIT 49x49 Reflectance Maps Reflectance map For a given viewing direction For each normal direction For each incoming direction (hemispherical integral) Evaluate reflection equation Reflection functions Diffuse: Irradiance map Glossy: Radiance map Anisotropic: for each tangent direction Mirror: Reflection map related to environment map Illumination functions Environment maps Procedural light sources Page 5

6 Quake Light Maps * Lower resolution Illumination Maps * = reflectance irradiance radiosity Page 6

7 Shadow Maps May incorporate shadow maps into lighting calculations Correct Shadow Maps Step 1: Create z-buffer of scene as seen from light source Step 2. Render scene as seen from the eye For each light Transform point into light coordinates return (zl < zbuffer[xl][yl] )? 1 : 0 Page 7

8 Displacement/Bump Mapping Offset surface position Displacement P (u, v) = P(u,v) + h(u, v)n( u,v) Perturb normal P(u, v) N(u,v) = u P(u,v) v From Blinn 1976 Shading and Texturing Language Flexibility Create procedural texture models Modulate multiple parameters Control over mapping Texture access float/color texture( image, s, t,...) point bump( heights, N, Ps, Pt, s, t,...) float/color environment( cubefaces, D,...) float shadow( depths, P,...) Page 8

9 Abstract Shading Model Volume Atmosphere Light Source Camera Surface Reflection Volume Texture Displacement Volume Deformation Light Surface Camera Light Shader State L N light bulb( float intensity = 1; color filament = TUNGSTEN ) { illuminate( P ) Cl = intensity * filament / (L.L); } Pu P,(u,v),.. Pv Page 9

10 Barzel s UberLight.sl Inconsistent Shadows Projected Shadow Matte Projected Texture Example of a complex shader UberLight( ) { Clip to near/far planes Clip to shape boundary foreach superelliptical blocker atten *= foreach cookie texture atten *= foreach slide texture color *= foreach noise texture atten, color *= foreach shadow map atten, color *= Calculate intensity fall-off Calculate beam distribution } Surface Shader N L surface diffuse() { color Ci = 0; illuminance( P, N, Pi/2 ) Ci += Cs * Cl * N.L; } I Pu P,u,v,.. Pv Page 10

11 RenderMan Surface Shader surface corrode(float Ks=0.4, Ka=0.1, rough=0.25) { float i, freq=1, turb=0; // compute fractal texture for( i=0; i<6; i++ ) { turb += 1/freq*noise(freq*P); freq *= 2; } // perturb surface P -= turb * normalize(n); N = faceforward(normalize(calculatenormal(p))); } // compute reflection and final color Ci = Cs*(Ka*ambient()+Ks*specular(N,I,rough)); Perlin s Noise Function 1. Generate a table of random numbers 2. Hash a 3D lattice into a table entry 3. Use random values as the gradient 4. Perform cubic interpolation Page 11

12 Turbulence fbm // compute fractal texture for( i=0; i<6; i++ ) { turb += 1/freq*noise(freq*P); freq *= 2; } = Images from Examples Wood and Stone RenderMan Companion Marble Ken Perlin Page 12

13 Examples (continued) Cloud David Ebert Page 13